Locally Asymptotic Stability of PDS Controller for Two-Link Flexible Arm

Abstract

We discuss the controller design and stability of closed-loop system for two-link flexible arm. The flexible arm is modeled as distributed parameter systems, which is infinite dimensional. In general, a controller for such distributed parameter systems is designed based on a finite dimensional approximated model. Therefore we should consider spillover instability that is the drawback resulting from finite dimensional approximation. In this paper, as we design the controller based on an original distributed parameter model, we can avoid the drawback. At first, using Lyapunov method, we derive a PDS feedback controller that the closed-loop system becomes Lyapunov stable. Note that the proposed PDS controller differs from the conventional PDS controller. The conventional PDS controller works well in neighborhood of a desired configuration of the arm, but the pro-posed PDS controller can ensure global stability. Next, we prove that the proposed PDS controller can ensure the asymptotic stability of the closed-loop system at the neighborhood of the desired configuration of the arm. The proof is completed using LaSalle's invariance principle, which is extended to infinite dimensional systems. Finally, in order to demonstrate the validity of the proposed controller, experiments have been carried out.